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The equation of motion gives x=(L/6)(V/3H^2) and has a solution x=([(1+y)^2+2 L/3]^{1/2}-(1+y))/2 where y\\equiv \\rmm/V and L= (V'/V)^2 (1+q)^2, q=\\ddotphi/V'. The resulting EoS is w=[6+ L- 6 \\sqrt((1+y)^2+2L/3)]/(L+6y). Since the universe is accelerating at present time we use the slow roll approximation in which case we have |q|<< 1 and L\\simeq (V'/V)^2. However, the derivation of w is exact "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.04439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-11-12T23:48:17Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"b49cc68f9f6fd074832f2913c230c227dc09de392d8f48898cb2a8fea1e7328c","abstract_canon_sha256":"e4d008880bf8ff04bc444f4dc8ea35fa9c36ee08f2109642743c7fdaffcc54b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:17.208990Z","signature_b64":"iEhAB4P7H9cBiEL684U+RWQEAb1I0ocH9i8PAz4lztDy/yMkg6cWvAQ3ZgbDhzDiiautpI81FR90+F/7KpvzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"887dab0d754eba1bf456f4fbae5a3a5992194ca11b3612e78491d79256433179","last_reissued_at":"2026-05-18T01:16:17.208373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:17.208373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dark Energy Parametrization motivated by Scalar Field Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"Axel de la Macorra","submitted_at":"2015-11-12T23:48:17Z","abstract_excerpt":"We propose a new Dark Energy parametrization based on the dynamics of a scalar field. We use an equation of state w=(x-1)/(x+1), with x=E_k/V, the ratio of kinetic energy E_k=\\dotphi^2/2 and potential V. The equation of motion gives x=(L/6)(V/3H^2) and has a solution x=([(1+y)^2+2 L/3]^{1/2}-(1+y))/2 where y\\equiv \\rmm/V and L= (V'/V)^2 (1+q)^2, q=\\ddotphi/V'. The resulting EoS is w=[6+ L- 6 \\sqrt((1+y)^2+2L/3)]/(L+6y). Since the universe is accelerating at present time we use the slow roll approximation in which case we have |q|<< 1 and L\\simeq (V'/V)^2. 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